1. Technical Field
The present invention relates to communication techniques and has been developed with particular attention paid to its possible use in communications systems that are able to support high data rates on different transmission channels (for example, power lines, wireless channels, etc.).
The description of the present application is made with reference to the documents that appear in the section entitled “References” at the foot of the description. In order not to burden the treatment, in the course of the description said documents are designated by a number in square brackets (for example, [X]), which enables identification of each document appearing in the list of references.
2. Description of the Related Art
The need to have available communications systems of the type outlined previously has increased considerably over the years. For this purpose, the world of research and design in the communications sector (for example, in the modem sector) has oriented its attention towards multi-carrier-modulation (MCM) techniques such as multiplex schemes of the discrete multi-tone (DMT) or orthogonal-frequency-division-multiplexing (OFDM) type.
Instead of employing single-carrier modulation with a very complex adaptive equalizer, the fact of employing an MCM technique with a channel divided into N subchannels means that the subchannels are basically independent Gaussian channels free from intersymbol interference (ISI). As illustrated in [1], another advantage of MCM techniques as compared to single-carrier systems lies in the considerable immunity in regard to impulsive noise and fast-fading phenomena. In MCM systems, each subchannel (or subcarrier, in what follows the two terms will be considered in effect to be equivalent) can be “loaded” in a different way, and the number of bits per subcarrier can be chosen as a function of the signal-to-noise ratio (SNR) estimated on each subcarrier prior to transmission of the data. Typically, the subcarriers with low signal-to-noise ratio are loaded with an accordingly reduced number of bits, there being associated thereto more robust modulations (for example, BPSK, 4-QAM, etc.). The subcarriers with higher signal-to-noise ratio are loaded with a larger number of bits, there being associated therewith modulations of higher order (for example 256-QAM, 1024-QAM, etc.). Said criteria are illustrated, for example, in [2].
The process that associates with each available subcarrier the number of bits to be transmitted or, equivalently, the size of the constellation amongst the constellations available is referred to as “bit-loading”.
In order to enhance the reliability of the communication, a coding is used during transmission. Coding introduces redundancy in the information sent over the communication channels in order to determine correctly the data in the presence of errors during transmission. As regards the coding techniques, block coding and convolutional coding are amongst the most frequently used ones. In particular, a few years ago a new class of codes, referred to as “turbo codes”, was introduced, which are based upon the parallel concatenation of two recursive convolutional codes separated by an interleaver of a turbo type, as described in [3], which demonstrates the possibility of obtaining levels of performance that approach the Shannon limit.
Thanks to this exceptional performance, the turbo codes have found many applications. Amongst the most recent there may be mentioned, for example, the use of OFDM schemes that employ QAM modulations subjected to turbo convolutional coding in the WiMax (see [4]) and HomePlug AV (HPAV) (see [5] and [6]) contexts.
In the past, the problem of bit-loading has been tackled using fundamentally two different optimization techniques, which lead to two types of approaches, referred to, respectively, as “rate-adaptive” and “margin-adaptive” [8].
The rate-adaptive solutions (see, for example, [9] and [10]) aim at maximizing the overall throughput of the system with a constraint on the transmission power. The solutions of a margin-adaptive type (as described, for example, in [11], [12], and [13]) aim, instead, at minimizing the transmission power with a constraint on the overall throughput of the system. Both types of solution are based upon the possibility of redistributing the power and the bits over the various OFDM subcarriers as a function of the estimated signal-to-noise ratio.
Communications systems can be on the other hand be subject to limitations of a normative type, which do not enable exploitation of schemes of power re-allocation. A typical example of this is the HPAV system referred to previously. It follows that the two approaches described above cannot be applied to systems of this type.
There have recently been proposed (see [14]) two bit-loading techniques of a discrete iterative and rate-adaptive type, with a non-adaptive power allocation, within the framework of an uncoded wireless system.
In [15] two different bit-loading techniques are described, with uniform power allocation, once again for an uncoded HPAV system. All these solutions aim at maximizing the overall throughput of the system, at the same time guaranteeing that the bit-error rate (BER) remains below a given threshold. However, when applied to a coded system, these techniques do not exploit the error-correction capabilities of the code, which means that the target BER is satisfied with ample margin, but at the expense of a reduction in terms of throughput. In the context of bit-loading and coding it may in fact be noted that the problem of maximizing the throughput and of obtaining in the meantime a target BER is frequently tackled by adapting the power and transmission mode, i.e., the rate of the encoder and the size of the constellation (see in this connection [16] and [17]). In this case, each subcarrier or a block of adjacent subcarriers is selected, and, on the basis of the channel characteristics, a transmission mode for the entire block is chosen taking into account the constraints imposed by the system.
Even though it is possible to combine bit-loading with coding, none of these techniques can be applied to systems that do not allow exploitation of power re-allocation.
Documents such as [18], [19], [20], [21], and [22] refer to yet another approach, in which an attempt is made to extend to a coded MCM system the classic bit-loading formula for an uncoded system, as defined in [11]:
                              b          k                =                                            log              2                        ⁡                          (                              1                +                                                      SNR                    k                                    Γ                                            )                                .                                    (        1        )            where bk and SNRk are, respectively, the number of bits to be loaded and the signal-to-noise ratio estimated on the subcarrier k, and
                    Γ        =                                                            (                                                      Q                                          -                      1                                                        ⁡                                      (                                          SER                      4                                        )                                                  )                            2                        3                    ⁢                      γ            m                                              (        2        )            is the SNR gap calculated starting from the target symbol-error rate (SER) using the Gaussian complementary distribution function given by
      Q    ⁡          (      x      )        =            1                        2          ⁢          π                      ⁢                  ∫        x                  +          ∞                    ⁢              Exp        ⁢                                  ⁢                  (                      -                                          z                2                            2                                )                ⁢                  ⅆ          z                    where γm is a margin introduced to take into account intrinsic system problems such as the presence of impulsive noise, the variance of the SNR estimate and other elements.
In the extension proposed for coded systems in [18], [19], [20], [21], and [22], the SNR gap is modified to
                    Γ        =                                                                              (                                                            Q                                              -                        1                                                              ⁡                                          (                                              SER                        4                                            )                                                        )                                2                            3                        ⁢                          γ              m                                            γ            c                                              (        3        )            where the term γc represents the coding gain.
Documents such as [23] highlight, however, the fact that this empirical approach is an obstacle to precision in determination of the constellation, in particular when the coding gain exhibits a high variability as a function of the size of the constellation.
Amongst the works that attempt to combine more efficiently the two concepts of bit-loading and coding, it is possible to cite [24], as regards the Reed-Solomon coding systems, and [25], as regards finite-impulse-response (FIR) codes such as common block codes and non-recursive convolutional codes. Analyzed in [26] is the performance of an LDPC-coded OFDM system with adaptive bit-loading based upon mutual information, given that the mutual information provides a characterization of the performance of LDPC-coded modulation systems. Presented in [23] is a bit-loading method based upon the calculation of a so-called input-output weight enumerating function (IOWEF) of the code for systems that enable a decoding of a soft type.
The authors of [23] have noted that this method proves effective if applied to systems with convolutional codes subject to Viterbi decoding or with BCH codes decoded with Chase decoding and also in the case of turbo product codes with serially concatenated BCH codes.
There exists, however, an intrinsic difficulty in identifying the exact theoretical performance of the coding and in correlating it directly to the performance in the uncoded case. This means that this solution does not operate in a satisfactory way with traditional turbo codes (such as the ones presented in [3]) or with non-binary turbo codes (such as the ones presented in [27]) or else with multidimensional turbo codes (such as the ones presented in [28]).
Described in [29] is a bit-loading method for turbo codes in a multichannel system. The corresponding method is characterized by two steps:
i)—application of the algorithm referred to as BER-threshold-constrained (BTC) algorithm (see [15]); and
ii)—application, during allocation, of the relation bk,p=bk,q. In this case, bk is the number of bits allocated on the subcarrier k after application of the previous step, and said term bk can be seen as the sum of three terms: bk=bk,s+bk,p+bk,q, where bk,s is the number of information bits, bk,p is the number of parity bits linked to the first, constituent, encoder, and bk,q is the number of parity bits linked to the second, constituent, encoder.
The BTC algorithm described in [15] applied in the first step is a classic traditional starting point for various bit-loading algorithms, such as the ones described in [30], [31], and [32]. However, as has already been said, it does not enable a complete exploitation of the code correction capabilities.
The refinement achieved with step ii) is interesting given that it enables balancing of the quality of the parity log-likelihood ratios (LLRs) at input to two decoders of the soft-input/soft-output (SISO) type that constitute the turbo decoder, maximizing their co-operation. However, the corresponding algorithm proves conservative in terms of BER, thus penalizing the throughput performance. In addition, if it is taken into account that the communications systems adopt a channel interleaver to cope with burst noise, the intrinsic suggestion in point ii) seen above better suits to the design of the channel interleaver than to the bit-loading technique. This in so far as, at a bit-loading level, there arises the unnecessary additional complication of distinguishing the bits generated by the two constituent encoders.
From the foregoing description, the present applicant has reasons to believe that there is still felt the need to have available a bit-loading technique that is truly efficient and satisfactory (in particular, in terms of throughput) in the case of systems with MCM turbo coding.